China Southern has a deal on to New York. The flight has a stopover in Guangzhou so it takes longer, but it is less than half the price of Air NZ.
Auckland to New York Flights from $1128 on China Southern
Sample travel dates:
Dep. Mon 07/Mar/16 Ret. Mon 21/Mar/16 $1,128
Dep. Wed 09/Mar/16 Ret. Wed 23/Mar/16 $1,128
Dep. Wed 19/Oct/16 Ret. Wed 26/Oct/16 $1,128
China Southern also fly to Chicago, Boston and Toronto but I wasn't able to find any comparable deals for those destinations. Let me know if you do & I'll update this deal.